The beauty of math; the humor of stupidity.

Tag Archives: global warming

Aside from the endless stream of Cantor cranks, the next biggest category of emails I get is from climate “skeptics”. They all ask pretty much the same question. For example, here’s one I received today:

My personal analysis, and natural sceptisism tells me, that there are something fundamentally wrong with the entire warming theory when it comes to the CO2.

If a gas in the atmosphere increase from 0.03 to 0.04… that just cant be a significant parameter, can it?

I generally ignore it, because… let’s face it, the majority of people who ask this question aren’t looking for a real answer. But this one was much more polite and reasonable than most, so I decided to answer it. And once I went to the trouble of writing a response, I figured that I might as well turn it into a post as well.

The current figures – you can find them in a variety of places from wikipedia to the US NOAA – are that the atmosphere CO2 has changed from around 280 parts per million in 1850 to 400 parts per million today.

Why can’t that be a significant parameter?

There’s a couple of things to understand to grasp global warming: how much energy carbon dioxide can trap in the atmosphere, and hom much carbon dioxide there actually is in the atmosphere. Put those two facts together, and you realize that we’re talking about a massive quantity of carbon dioxide trapping a massive amount of energy.

The problem is scale. Humans notoriously have a really hard time wrapping our heads around scale. When numbers get big enough, we aren’t able to really grasp them intuitively and understand what they mean. The difference between two numbers like 300 and 400ppm is tiny, we can’t really grasp how in could be significant, because we aren’t good at taking that small difference, and realizing just how ridiculously large it actually is.

If you actually look at the math behind the greenhouse effect, you find that some gasses are very effective at trapping heat. The earth is only habitable because of the carbon dioxide in the atmosphere – without it, earth would be too cold for life. Small amounts of it provide enough heat-trapping effect to move us from a frozen rock to the world we have. Increasing the quantity of it increases the amount of heat it can trap.

Let’s think about what the difference between 280 and 400 parts per million actually means at the scale of earth’s atmosphere. You hear a number like 400ppm – that’s 4 one-hundreds of one percent – that seems like nothing, right? How could that have such a massive effect?!

But like so many other mathematical things, you need to put that number into the appropriate scale. The earths atmosphere masses roughly 5 times 10^21 grams. 400ppm of that scales to 2 times 10^18 grams of carbon dioxide. That’s 2 billion trillion kilograms of CO2. Compared to 100 years ago, that’s about 800 million trillion kilograms of carbon dioxide added to the atmosphere over the last hundred years. That’s a really, really massive quantity of carbon dioxide! scaled to the number of particles, that’s something around 10^40th (plus or minus a couple of powers of ten – at this scale, who cares?) additional molecules of carbon dioxide in the atmosphere. It’s a very small percentage, but it’s a huge quantity.

When you talk about trapping heat, you also have to remember that there’s scaling issues there, too. We’re not talking about adding 100 degrees to the earths temperature. It’s a massive increase in the quantity of energy in the atmosphere, but because the atmosphere is so large, it doesn’t look like much: just a couple of degrees. That can be very deceptive – 5 degrees celsius isn’t a huge temperature difference. But if you think of the quantity of extra energy that’s being absorbed by the atmosphere to produce that difference, it’s pretty damned huge. It doesn’t necessarily look like all that much when you see it stated at 2 degrees celsius – but if you think of it terms of the quantity of additional energy being trapped by the atmosphere, it’s very significant.

Calculating just how much energy a molecule of CO2 can absorb is a lot trickier than calculating the mass-change of the quantity of CO2 in the atmosphere. It’s a complicated phenomenon which involves a lot of different factors – how much infrared is absorbed by an atom, how quickly that energy gets distributed into the other molecules that it interacts with… I’m not going to go into detail on that. There’s a ton of places, like here, where you can look up a detailed explanation. But when you consider the scale issues, it should be clear that there’s a pretty damned massive increase in the capacity to absorb energy in a small percentage-wise increase in the quantity of CO2.

I’ve been trapped in post-storm hell (no power, no heat for 10 days. Now power is back, but still no internet at home, which is frustrating, but no big deal), and so I haven’t been able to post this until now.

I’ve been getting a bunch of questions from people in response to an earlier post of mine about global warming, where I said that we can’t blame specific weather events on global warming. The questions come down to: “Can we say that hurricane Sandy and yesterday’s NorEaster were caused by global warming?”

I try to be really careful about things like this. Increasing the amount of energy in the environment definitely has an effect on weather patterns. But for the most part, that effect is statistical. That is, we can’t generally say that a specific extreme weather event wouldn’t have happened without global warming. We can just say that we expect extreme weather events to become much more common.

But what about hurricane Sandy?

Yes, it was caused by global warming.

How can I say that so definitively?

There were a lot of observations made around this particular hurricane. What made it such a severe event is a combination of three primary factors.

The ocean water over which it developed is warmer that historically normal. Warm water is, simply, fuel for hurricanes. We know this from years of observation. And we know that the water was warmer, by a couple of degrees, than it would normally be in this season. This is a direct cause for the power of the storm, for the fact that as it moved north, it continued to become stronger rather than weakening. Those warm waters are, by definition global warming: they’re one of the things we measure when we’re measuring global temperature trends.

Hurricane Sandy took a pretty dramatic left turn as it came north, which is what swept it into the east coast of the US. That is a very unusual trajectory. Why did it do that? Because of an unusual weather pattern in the Northeast Atlantic, called a negative North Atlantic oscillation (-NAO). And where did the -NAO come from? Our best models strongly suggest that it resulted, at least in part, from icemelt from Greenland. This is less certain than the first factor, but still likely enough that we can be pretty confident.

Hurricane Sandy merged with another weather front as it came inland, which intensified it as it came ashore. This one doesn’t have any direct relation to global warming: the front that it merged with is typical autumn weather on the east coast.

So of the three factors that caused the severe hurricane, one of them is absolutely, undeniably global warming. The second is very probably linked to global warming. And the third isn’t.

This is important to understand. We shouldn’t make broad statements about causation when we can’t prove them. But we also shouldn’t refrain from making definitely statements about causation when we can.

The NorEaster that we’re now recovering from falls in to that first class. We simply don’t know if it would have happened without the hurricane. The best models that I’ve seen suggest that it probably wouldn’t have happened without the effects of the earlier hurricane, but it’s just not certain enough to draw a definitive conclusion.

But the Hurricane? There is absolutely no way that anyone can honestly look at the data, and conclude that it was not caused by warming. Anyone who says otherwise is, quite simply, a liar.

Like this:

Global warming is a big issue. If we’re honest and we look carefully at the data, it’s beyond question that the atmosphere of our planet is warming. It’s also beyond any honest question that the preponderance of the evidence is that human behavior is the primary cause. It’s not impossible that we’re wrong – but when we look at the real evidence, it’s overwhelming.

Of course, this doesn’t stop people from being idiots.

But what I’m going to focus on here isn’t exactly the usual idiots. See, here in the US, we’re in the middle of a dramatic heat wave. All over the country, we’ve been breaking heat daily temperature records. As I write this, it’s 98 degrees outside here in NY, and we’re expecting another couple of degrees. Out in the west, there are gigantic wildfires, cause by poor snowfall last winter, poor rainfall this spring, and record heat to dry everything out. So: is this global warming?

We’re seeing lots and lots of people saying yes. Or worse, saying that it is, because of the heat wave, while pretending that they’re not really saying that it is. For one, among all-too-many examples, you can look at Bad Astronomy here. Not to rag too much on Phil though, because hes just one among about two dozen different example of this that I’ve seen in the last 3 days.

Weather 10 or twenty degree above normal isn’t global warming. A heat wave, even a massive epic heat wave, isn’t proof that global warming is real, any more than an epic cold wave or blizzard is evidence that global warming is fake.

I’m sure you’ve heard many people say weather is not climate. But for human beings, it’s really hard to understand just what that really means. Climate is a world-wide long-term average; weather is instantaneous and local. This isn’t just a nitpick: it’s a huge distinction. When we talk about global warming, what we’re talking about is the year-round average temperature changing by one or two degrees. A ten degree variation in local weather doesn’t tell us anything about the worldwide trend.

Global warming is about climate. And part of what that means is that in some places, global warming will probably make the weather colder. Cold weather isn’t evidence against global warming. Most people realize that – which is why we all laugh when gasbags like Rush Limbaugh talk about how a snowstorm “proves” that global warming is a fraud. But at the same time, we look at weather like what we have in the US, and conclude that “Yes, global warming is real”. But we’re making the same mistake.

Global warming is about a surprisingly small change. Over the last hundred years, global warming is a change of about 1 degree celsius in the global average temperature. That’s about 1 1/2 degrees fahrenheit, for us Americans. It seems miniscule, and it’s a tiny fraction of the temperature difference that we’re seeing this summer in the US.

But that tiny difference in climate can cause huge differences in weather. As I mentioned before, it can make local weather either warmer or colder – not just by directly warming the air, but by altering wind and water currents in ways that create dramatic changes.

For example, global warming could, likely, make Europe significantly colder. How? The weather in western Europe is greatly affected by an ocean water current called the atlantic conveyor. The conveyor is a cyclic ocean current, where (driven in part by the jet stream), warm water flows north from the equator in a surface current, cooling as it goes, until it finally sinks and starts to cycle back south in a deep underwater current. This acts as a heat pump, moving energy from the equator north and east to western Europe. This is why Western Europe is significantly warmer than places at the same latitude in Eastern North America.

Global warming could alter the flow of the atlantic conveyor. (We don’t know if it will – but it’s one possibility, which makes a good example of something counter-intuitive.) If the conveyor is slowed, so that it transfers less energy, Europe will get colder. How could the conveyor be slowed? By ice-melt. The conveyor works as a cycle because of the differences in density between warm and cold water: cold water is denser than warm water, so the cold water sinks as it cools. It warms in the tropics, gets pushed north by the jet stream, cools along the way and gradually sinks.

But global warming is melting a lot of artic and glacier ice, which produces freshwater. Freshwater is less dense than saltwater. So the freshwater, when it dilutes the cold water at the northern end of the conveyor, it reduces its density relative to the pure salt-water – and that reduces the tendency of the cold water to sink, which could slow the conveyor.

There are numerous similar phenomena that involve changes in ocean currents and wind due to relatively small temperature variations. El Nino and La Nina, conveyor changes, changes in the moisture-carrying capacity of wind currents to carry – they’re all caused by relatively small changes – changes well with the couple of degrees of variatio that we see occuring.

But we need to be honest and careful. This summer may be incredibly hot, and we had an unsually warm winter before it – but we really shouldn’t try to use that as evidence of global warming. Because if you do, when some colder-than-normal weather occurs somewhere, the cranks and liars that want to convince people that global warming is an elaborate fraud will use that the muddle things – and when they do, it’ll be our fault when people fall for it, because we’ll be the ones who primed them for that argument. As nice, as convenient, as convincing as it might seem to draw a correlation between a specific instance of extreme weather and global warming, we really need to stop doing it.